Solve the following triangles:
13. A side and a diagonal of a parallelogram are 12 inches and 19 inches respectively. The angle between the diagonals, opposite the given side, is 124°. Find the length of the other diagonal and the length of the other side.
14. A lighthouse is 10 miles northeast of a dock. A ship leaves the dock at noon, and sails east at a speed of 12 miles an hour. At what time will it be 8 miles from the lighthouse?
15.A vertical pole 35 feet high, standing on sloping ground, is braced by a wire which extends from the top of the pole to a point on the ground 25 feet from the foot of the pole. If the pole. subtends an angle of 30° at the point where the wire reaches the ground, how long is the wire?
16.A tower 125 feet high stands on the side of a hill. At a point 240 feet from the foot of the tower, measured straight down the hill, the tower subtends an angle of 25°. What angle does the side of the hill make with the horizontal?
(13)
Let b Side adjacent to angle of
Using cosine rule
or
Length of the diagonal
(14)
Let b distance sailed.
Using cosine Rule
Time taken
Or
Time can be
(15)
Let b length of the wire
Using cosine rule
Length of the wire
(16)
From a triangle 240 feet opposite to and 125 feet opposite to
Let angle to horizontal
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